Is your plinth made from stainless steel or regular steel. If it is made from stainless steel, depending on who finished it and where, your brushed finish may have been done with a mild steel wire brush. If it was done this way, then mild steel which rusts has been burnished into the stainless steel which is rust resistant. I would advise using a product like CLR or other rust removing chemical to remove the rust. This unfortunately will not remove the mild steel burnished into the surface of the plinth. Which means that there is a good chance the you will be removing rust from the plinth again at sometime in the future. Mild steel brushes are frequently used to achieve a brushed finish on stainless steel because they are cheaper to buy then a stainless brush, which is what should have been used to achieve the brushed appearance.
Scotty